if log0.3(x-1) < log0.09(x-1), then x lies in the interval....

AAYUSH,....THANKS FOR YOUR EFFORT BUT THE SOLUTION IS WRONG........

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log0.3 (x-1) < log0.09 (x-1)

log0.3 (x-1) < log(0.3)^2 (x-1)

log0.3 (x-1) < 1/2 log0.3 (x-1)
2log0.3 (x-1) < log0.3 (x-1)
(x-1)^2>x-1
x>2
(2, infinity)
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But why the sign of inequality has changed
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his answer is right
there is one more domain that is (x-1)>0
 
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Sign of inquality has changed because base is less than 1
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Wrong answer 😟😟😟😟😟
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Please find this answer

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Attached below is the solution.

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Please find this answer

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